Method for measuring pose of robotic end tool

ABSTRACT

A method for measuring a pose of a robotic end tool, including: obtaining a three-dimensional feature of a flange and a three-dimensional feature of the end tool, establishing a first coordinate system and a second coordinate system at the center of the flange and the center of the end tool respectively, calculating a positional offset of the second coordinate system relative to the first coordinate system, and calculating a rotation offset of the second coordinate system relative to the first coordinate system according to each unit vector of the second coordinate system, so as to obtain a pose of the end tool relative to the flange. The method provided in the present application, compared with the manual observation method, the precision and stability of the pose measurement method are high.

FIELD

The present application relates to the field of industrial robots, andmore particularly relates to a method for measuring a pose of a roboticend tool.

BACKGROUND

With the development of high-end manufacturing, the requirement ofmachining precision of industrial robots is getting higher and higher.When using industrial robots to machine corresponding products, it isnecessary to place machining tools such as welding guns and cutters atthe end of the industrial robot. The precision of pose calibration of atool center point directly affects the machining precision of theindustrial robot. Herein, the pose refers to the position and posture ofthe end tool of the industrial robot in a specified coordinate system.

After the industrial robot is replaced with a new tool or after a longperiod of operation, a certain deviation of the center point of the toolwill occur, resulting in a lowered machining precision of the robot.Therefore, it is necessary to measure the center point of the roboticend tool and perform deviation compensation. At present, for themeasurement of the center point pose of the robotic end tool, the methodof manual observation is usually adopted, and the multi-pose isapproached to affixed point to realize the measurement of the centerpoint pose of the end tool. However, this method relies on manualmovement and visual observation, and its precision and stability arelow.

SUMMARY

An object of the present application is to provide a method formeasuring the pose of a robotic end tool, in order to solve thetechnical problem that the center point pose measurement of the roboticend tool in the prior art is low in precision and stability caused bythe manual method.

The present application provides a method for measuring a pose of arobotic end tool, comprising the following steps:

obtaining a three-dimensional feature of a flange for clamping the endtool and a three-dimensional feature of the end tool;

determining a center of the flange according to the three-dimensionalfeature of the flange, determining a center of the end tool according tothe three-dimensional feature of the end tool;

establishing a first coordinate system and a second coordinate systembased on the center of the flange and the center of the end toolrespectively;

calculating a positional offset of an origin of the second coordinatesystem relative to an origin of the first coordinate system;

calculating in the first coordinate system, a unit vector of a positivedirection of the X-axis of the second coordinate system, a unit vectorof a positive direction of the Y-axis, and a unit vector of a positivedirection of the Z-axis in the first coordinate system, calculating aunit vector of a positive direction of the X-axis, a unit vector of apositive direction of the Y-axis, and a unit vector of a positivedirection of the Z-axis of the second coordinate system; and forming aposture transformation matrix of the second coordinate system by theunit vector of the positive direction of the X-axis, the unit vector ofthe positive direction of the Y-axis, and the unit vector of thepositive direction of the Z-axis of the second coordinate system incommonly form a posture transformation matrix of the second coordinatesystem, and calculating a rotation offset of the second coordinatesystem relative to the first coordinate system by the posturetransformation matrix.

Further, the specific steps of calculating the positional offset of theorigin of the second coordinate system relative to the origin of thefirst coordinate system comprising:

The origin of the first coordinate system is defined as 0₁, the originof the second coordinate system is defined as 0₂, and the coordinatevalue of 0₁ in the first coordinate system is defined as (0, 0, 0), andthe coordinate value of 0₂ in the first coordinate system is defined as(x₀, y₀, z₀);

Calculating the positional offset as Δx=x₀, Δy=y₀, Δz=z₀: wherein the Δxis the positional offset of the second coordinate system relative to thefirst coordinate system in the X direction, the Δy is the positionaloffset of the second coordinate system relative to the first coordinatesystem in the Y direction, and the Δz is the positional offset of thesecond coordinate system relative to the first coordinate system in theZ direction.

Further, the step that in the first coordinate system, calculating aunit vector of a positive direction of the X-axis of the secondcoordinate system, a unit vector of a positive direction of the Y-axis,and a unit vector of a positive direction of the Z-axis specificallycomprising:

taking Points P₁ and P₂ on the X-axis and the Y-axis of the secondcoordinate system respectively, and the coordinate values of P₁ and P₂in the first coordinate system are defined as (x₁, y₁, z₁) and (x₂, y₂,z₂) respectively;

calculating the vector {right arrow over (O₂P₁)}=(x₁−x₀, y₁−y₀, z₁−z₀),and calculating the vector {right arrow over (O₂P₂)}=(x₂−x₀, y₂−y₀,z₂−z₀);

calculating a unit vector {right arrow over (X)} of the {right arrowover (O₂P₁)} as

$\left( {\frac{x_{1} - x_{0}}{\sqrt{\left( {x_{1} - x_{0}} \right)^{2} + \left( {y_{1} - y_{0}} \right)^{2} + \left( {z_{1} - z_{0}} \right)^{2}}},\frac{y_{1} - y_{0}}{\sqrt{\left( {x_{1} - x_{0}} \right)^{2} + \left( {y_{1} - y_{0}} \right)^{2} + \left( {z_{1} - z_{0}} \right)^{2}}},\frac{z_{1} - z_{0}}{\sqrt{\left( {x_{1} - x_{0}} \right)^{2} + \left( {y_{1} - y_{0}} \right)^{2} + \left( {z_{1} - z_{0}} \right)^{2}}}} \right)$wherein the {right arrow over (X)} is a unit vector of the secondcoordinate system in the positive direction of the X-axis;

calculating a unit vector {right arrow over (Y)} of the {right arrowover (O₂P₂)} as

$\left( {\frac{x_{2} - x_{0}}{\sqrt{\left( {x_{2} - x_{0}} \right)^{2} + \left( {y_{2} - y_{0}} \right)^{2} + \left( {z_{2} - z_{0}} \right)^{2}}},\frac{y_{2} - y_{0}}{\sqrt{\left( {x_{2} - x_{0}} \right)^{2} + \left( {y_{2} - y_{0}} \right)^{2} + \left( {z_{1} - z_{0}} \right)^{2}}},\frac{z_{2} - z_{0}}{\sqrt{\left( {x_{1} - x_{0}} \right)^{2} + \left( {y_{1} - y_{0}} \right)^{2} + \left( {z_{2} - z_{0}} \right)^{2}}}} \right)$wherein the {right arrow over (Y)} is a unit vector of the secondcoordinate system in the positive direction of the Y-axis;

calculating a unit vector {right arrow over (Z)} of the secondcoordinate system in the positive direction of the Z-axis as {rightarrow over (X)}×{right arrow over (Y)}.

Further, supposing the unit vector of the positive direction of theX-axis of the second coordinate system is (a₁, b₁, c₁), and the unitvector of the positive direction of the Y-axis of the second coordinatesystem is (a₂, b₂, c₂), the unit vector of the positive direction of theZ-axis of the second coordinate system is (a₃, b₃, c₃), and the posturetransformation matrix is calculated as

$\begin{bmatrix}a_{1} & a_{2} & a_{3} \\b_{1} & b_{2} & b_{3} \\c_{1} & c_{2} & c_{3}\end{bmatrix}.$

Further, the rotation offset are defined as

${R_{x} = {\tan^{- 1}\frac{b_{1}}{a_{1}}}},{R_{y} = {\tan^{- 1}\frac{- c_{1}}{\sqrt{a_{1}^{2} + b_{1}^{2}}}}},$

${R_{z} = {\tan^{- 1}\frac{c_{2}}{c_{3}}}},$wherein the R_(x) is a rotational offset of the second coordinate systemrelative to the first coordinate system on the X-axis, and the R_(y) isa rotational offset of the second coordinate system relative to thefirst coordinate system on the Y-axis, the R_(z) is a rotational offsetof the second coordinate system relative to the first coordinate systemon the Z-axis.

Further, obtaining the three-dimensional features of the flange and theend tool by a binocular three-dimensional scanner.

The beneficial effect of the method for measuring the pose of therobotic end tool provided by the present application is summarized asfollows: comparing to the prior art, the method for measuring the poseof the robotic end tool of the present application establishes a firstcoordinate system and a second coordinate system at the center of theflange and the center of the end tool respectively, calculates apositional offset of the origin of the second coordinate system relativeto the origin of the first coordinate system, and calculates arotational offset of the second coordinate system relative to the firstcoordinate system by the posture transformation matrix of the secondcoordinate system, therefore obtains the pose of the end tool relativeto the flange. The method for measuring the pose obtains the pose of theend tool by calculating the relative position and relative posture ofthe end tool and the flange, and compared with the manual observationmethod, the precision and stability of the pose measurement method arehigh.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to make the technical solutions in the embodiments of thepresent application clearer, the accompanying drawings to be used in theembodiments and the description of the prior art will be brieflyintroduced below, it is apparent that the drawings in the followingdescription are merely some embodiments of the present application andthat other drawings may be obtained by those skilled in the fieldwithout departing from the inventive nature of the application.

FIG. 1 is a flowchart of implement of a method for measuring the pose ofa robotic end tool according to an embodiment of the presentapplication;

FIG. 2 is a schematic diagram of a method for measuring the pose of arobotic end too according to an embodiment of the present application;

FIG. 3 is a schematic diagram of a first coordinate system and a secondcoordinate system used in the embodiment of the present application.

In the drawings, the following reference numerals are used:

-   -   1—binocular three-dimensional scanner; 2—robot; 21—flange;        210—first coordinate system; 22—end tool; and 220—second        coordinate system.

DETAILED DESCRIPTION

In order to make the technical problems to be solved, technicalsolutions, and beneficial effects of the present application clearer andmore understandable, the present application will be further describedin detail hereinafter with reference to the accompanying drawings andembodiments. It should be understood that the embodiments describedherein are only intended to illustrate but not to limit the presentapplication.

It should be noted that when a component is referred to as being “fixedto” or “disposed on” another component, it can be directly or indirectlyon another component. When a component is referred to as being“connected to” another component, it can be directly or indirectlyconnected to another component.

It should be understood that, “length”, “width”, “upper”, “lower”,“front”, “back”, “left” and “right”, “vertical”, “horizontal”, “top”,“bottom”, “inside”, “outside” and other terms indicating the orientationor positional relationship are based on orientation or positionalrelationship shown in the drawings, and are only for the purpose offacilitating the description of the application and simplifying thedescription, instead of indicating or implying that the indicated deviceor component must have a specific orientation and constructed andoperated in a particular orientation, and therefore it cannot beconstrued as limitation of the application.

In addition, the terms “first” and “second” are for illustrativepurposes only and should not be construed as indicating or implying arelative importance or implicitly indicating the quantity of technicalfeatures indicated. Therefore, a feature that defines “first” and“second” may expressly or implicitly include one or more of thefeatures. In the description of the present application, “multiple”means two or more than two, unless otherwise specifically defined.

Please refer to FIG. 1 and FIG. 2, the method for measuring the pose ofthe robotic end tool provided by the present application will now bedescribed. The robot 2 includes a robot arm, a flange 21 fixed to therobot arm, and an end tool 22 clamped at the flange 21, and the end tool22 comprises a welding gun, a cutter, and the like. The pose of therobotic end tool refers to the position and posture of the end tool 22in the specified coordinate system, and the position and posture of theend tool 22 can be used to represent as the position offset and therotational offset of the end tool 22 relative to the specifiedcoordinate system respectively. The method for measuring the posecomprises the following steps:

Step S101, which is specifically as follows:

a three-dimensional feature of the flange 21 for clamping the end tool22 and a three-dimensional feature of the end tool 22 are obtained, thatis, by obtaining an external contour lattice of the flange 21 and theend tool 22, the external contour lattice of the flange 21 are combinedto form the three-dimensional feature of the flange 21, the externalcontour lattices of the end tool 22 are combined to form athree-dimensional feature of the end tool 22.

Further, in step S101, the three-dimensional feature of the flange 21and the end tool 22 are obtained by the binocular three-dimensionalscanner 1. When the binocular three-dimensional scanner 1 is used, thebinocular three-dimensional scanner 1 is placed in the vicinity of therobotic end tool 22, and the external contour features of the end tool22 and the flange 21 are scanned to obtain the external contour latticeof the end tool 22 and the flange 21, then upload the data of theexternal contour lattice to a reverse engineering software, the unneededdata are deleted using the reverse engineering software, and then theline fitting and surface fitting of the remaining lattice data areperformed, and finally the three-dimensional feature is formed throughthe fitted line and surface.

Step S102, which is specifically as follows:

a center of the flange 21 is determined according to thethree-dimensional feature of the flange 21, a center of the end tool 22is determined according to the three-dimensional feature of the end tool22. When determining the center of the flange 21 and the center of theend tool 22, the external contour lattices are firstly processed byreverse engineering software such as Germanic, Image ware or the like,the unnecessary lattice data are deleted, and then line fitting andsurface fitting of the remaining lattice data are performed, and finallythe center of the end tools 22 and the center of the flange 21 aredetermined through the fitted line and surface.

Step S103, which is specifically as follows:

a first coordinate system 210 and a second coordinate system 220 areestablished based on the center of the flange 21 and the center of theend tool 22 respectively, and the first coordinate system 210 and thesecond coordinate system 220 are Cartesian rectangular coordinatesystems including mutually perpendicular X-axis, Y-axis and Z-axis;

Step S104, which is specifically as follows:

a positional offset of an origin of the second coordinate system 220relative to an origin of the first coordinate system 210 is calculated,herein, the positional offset refers to positional offsets of the originof the second coordinate system 220 relative to the origin of the firstcoordinate system 210 on the X-axis, the Y-axis, and the Z-axis,respectively.

Further, in step S104, as shown in FIG. 3, the origin of the firstcoordinate system 210 is defined as 0₁, the origin of the secondcoordinate system 220 is defined as 0₂, the coordinate value of 0₁ inthe first coordinate system 210 is defined as (0, 0, 0), and thecoordinate value of 0₂ in the first coordinate system 210 is defined as(x₀, y₀, z₀), the positional offset of the origin of the secondcoordinate system 220 relative to the origin of the first coordinatesystem 210 is defined as (Δx, Δy, Δz), wherein the Δx is the positionaloffset of the second coordinate system 220 relative to the firstcoordinate system 210 in the X direction, the Δy is the positionaloffset of the second coordinate system 220 relative to the firstcoordinate system 210 in the Y direction, and the Δz is the positionaloffset of the second coordinate system 220 relative to the firstcoordinate system 210 in the Z direction. So that Δx=x₀−0=x₀,Δy=y₀−0=y₀, Δz=z₀−0=z₀, it can be concluded that the positional offsetof the end tool 22 relative to the flange 21 is (x₀, y₀, z₀).

Step S105, which is specifically as follows:

In the first coordinate system 210, a unit vector of the positivedirection of the X-axis of the second coordinate system 220, a unitvector of the positive direction of the Y-axis, and a unit vector of thepositive direction of the Z-axis are calculated, the first coordinatesystem 210 is used as a reference coordinate system, and the straightlines of the X-axis, the Y-axis, and the Z-axis of the second coordinatesystem 220 all have a certain direction. The respective directions ofthe X-axis, the Y-axis, and the Z-axis of the second coordinate system220 can be represented by direction vectors, and the unit vectors of theX-axis, the Y-axis, and the Z-axis can be obtained by dividing eachdirection vector by the respective modular length.

Further, in step S105, please refer to FIG. 3, points P₁ and P₂ arerespectively taken from the X-axis and the Y-axis of the secondcoordinate system 220 respectively, and the coordinate values of P₁ andP₂ in the first coordinate system 210 are defined as (x₁, y₁, z₁) and(x₂, y₂, z₂) respectively; P₁ and P₂ are any points on the X-axis andthe Y-axis respectively; the vector direction of the directed linesegment O₂P₁ is the same as the vector direction of the positivedirection of the X-axis of the second coordinate system 220, and thevector direction of the directed line segment O₂P₂ is the same as thevector direction of the positive direction of the Y-axis of the secondcoordinate system 220,

So calculating the vector {right arrow over (O₂P₁)}=(x₁−x₀, y₁−y₌₀,z₁−z₀), the vector {right arrow over (O₂P₂)}=(x₂−x₀, y₂−y₀, z₂−z₀); anda unit vector {right arrow over (X)} of the {right arrow over (O₂P₁)} as

$\overset{\rightarrow}{X} = \left( {\frac{x_{1} - x_{0}}{\sqrt{\left( {x_{1} - x_{0}} \right)^{2} + \left( {y_{1} - y_{0}} \right)^{2} + \left( {z_{1} - z_{0}} \right)^{2}}},\frac{y_{1} - y_{0}}{\sqrt{\left( {x_{1} - x_{0}} \right)^{2} + \left( {y_{1} - y_{0}} \right)^{2} + \left( {z_{1} - z_{0}} \right)^{2}}},\frac{z_{1} - z_{0}}{\sqrt{\left( {x_{1} - x_{0}} \right)^{2} + \left( {y_{1} - y_{0}} \right)^{2} + \left( {z_{1} - z_{0}} \right)^{2}}}} \right)$a unit vector {right arrow over (Y)} of the {right arrow over (O₂P₂)} as

$\overset{\rightarrow}{Y} = \left( {\frac{x_{2} - x_{0}}{\sqrt{\left( {x_{2} - x_{0}} \right)^{2} + \left( {y_{2} - y_{0}} \right)^{2} + \left( {z_{2} - z_{0}} \right)^{2}}},\frac{y_{2} - y_{0}}{\sqrt{\left( {x_{2} - x_{0}} \right)^{2} + \left( {y_{2} - y_{0}} \right)^{2} + \left( {z_{2} - z_{0}} \right)^{2}}},\frac{z_{2} - z_{0}}{\sqrt{\left( {x_{2} - x_{0}} \right)^{2} + \left( {y_{2} - y_{0}} \right)^{2} + \left( {z_{2} - z_{0}} \right)^{2}}}} \right)$wherein the {right arrow over (X)} is the unit vector of the secondcoordinate system 220 in the positive direction of the X-axis, the{right arrow over (Y)} is the unit vector of the second coordinatesystem 220 in the positive direction of the Y-axis; the unit vector{right arrow over (X)} and the unit vector {right arrow over (Y)} areperpendicular to each other, according to the expressions of the {rightarrow over (X)} vector and the {right arrow over (Y)} vector, a {rightarrow over (Z)} vector perpendicular to the plane in which the {rightarrow over (X)} vector and the {right arrow over (Y)} vector are locatedcan be calculated, and the {right arrow over (Z)} vector is a unitvector in the positive direction of the Z-axis in the second coordinatesystem 220, supposing {right arrow over (X)}=(a₁,b₁,c₁), Y=(a₂,b₂,c₂),wherein:

${a_{1} = \frac{x_{1} - x_{0}}{\sqrt{\left( {x_{1} - x_{0}} \right)^{2} + \left( {y_{1} - y_{0}} \right)^{2} + \left( {z_{1} - z_{0}} \right)^{2}}}},{b_{1} = \frac{y_{1} - y_{0}}{\sqrt{\left( {x_{1} - x_{0}} \right)^{2} + \left( {y_{1} - y_{0}} \right)^{2} + \left( {z_{1} - z_{0}} \right)^{2}}}},$

${c_{1} = \frac{z_{1} - z_{0}}{\sqrt{\left( {x_{1} - x_{0}} \right)^{2} + \left( {y_{1} - y_{0}} \right)^{2} + \left( {z_{1} - z_{0}} \right)^{2}}}},{a_{2} = \frac{x_{2} - x_{0}}{\sqrt{\left( {x_{2} - x_{0}} \right)^{2} + \left( {y_{2} - y_{0}} \right)^{2} + \left( {z_{2} - z_{0}} \right)^{2}}}},{b_{2} = \frac{y_{2} - y_{0}}{\sqrt{\left( {x_{2} - x_{0}} \right)^{2} + \left( {y_{2} - y_{0}} \right)^{2} + \left( {z_{2} - z_{0}} \right)^{2}}}},{c_{2} = \frac{z_{2} - z_{0}}{\sqrt{\left( {x_{2} - x_{0}} \right)^{2} + \left( {y_{2} - y_{0}} \right)^{2} + \left( {z_{2} - z_{0}} \right)^{2}}}},$so {right arrow over (Z)}={right arrow over (X)}×{right arrow over(Y)}=(b₁,c₂−b₂c₁,a₁c₂−a₂c₁,a₁b₂−a₂b₁), according to the above steps, theunit vector of the X-axis positive direction, the Y-axis positivedirection, and the Z-axis positive direction in the second coordinatesystem 220 can be obtained.

Step S106 specifically is:

The unit vector of the positive direction of the X-axis, the unit vectorof the positive direction of the Y-axis, and the unit vector of thepositive direction of the Z-axis of the second coordinate system 220together form a posture transformation matrix of the second coordinatesystem 220, and a rotation offset of the second coordinate system 220relative to the first coordinate system 210 is calculated by the posturetransformation matrix.

Further, in step S106, the unit vector of the positive direction of theX-axis of the second coordinate system 220 is defined as {right arrowover (X)}=(a₁,b₁,c₁), and the unit vector of the positive direction ofthe Y-axis of the second coordinate system 220 is defined asY=(a₂,b₂,c₂), the unit vector of the positive direction of the Z-axis ofthe second coordinate system 220 is defined as {right arrow over(Z)}=(a₃,b₃,c₃), wherein a₃=b₁c₂−b₂c₁, b₃=a₁c₂−a₂c₁, c₃=a₁b₂−a₂b₁, andthe posture transformation matrix is calculated as

${\begin{bmatrix}a_{1} & a_{2} & a_{3} \\b_{1} & b_{2} & b_{3} \\c_{1} & c_{2} & c_{3}\end{bmatrix} = \begin{bmatrix}a_{1} & a_{2} & {{b_{1}c_{2}} - {b_{2}c_{1}}} \\b_{1} & b_{2} & {{a_{1}c_{2}} - {a_{2}c_{1}}} \\c_{1} & c_{2} & {{a_{1}b_{2}} - {a_{2}b_{1}}}\end{bmatrix}},$the posture transformation matrix may represent the posturetransformation of the second coordinate system 220 relative to the firstcoordinate system 210, that is, the posture transformation of the endtool 22 relative to the flange 21 may be indicated.

Further, in step S106, according to the posture transformation matrixcan obtain, the rotation offset of the second coordinate system 220relative to the first coordinate system 210, the rotation offset are

${R_{x} = {\tan^{- 1}\frac{b_{1}}{a_{1}}}},{R_{y} = {\tan^{- 1}\frac{- c_{1}}{\sqrt{a_{1}^{2} + b_{1}^{2}}}}},{R_{z} = {\tan^{- 1}\frac{c_{2}}{c_{3}}}},$wherein the R_(x) is a rotational offset of the second coordinate system220 relative to the first coordinate system 210 on the X-axis, and theR_(y) is a rotational offset of the second coordinate system 220relative to the first coordinate system 210 on the Y-axis, the R_(z) isa rotational offset of the second coordinate system 220 relative to thefirst coordinate system 210 on the Z-axis, and then substitutinga₃=b₁c₂−b₂c₁, b₃=a₁c₂−a₂c₁, c₃=a₁b₂−a₂b₁ into the expression of therotation offset, which can obtain

${R_{x} = {\tan^{- 1}\frac{b_{1}}{a_{1}}}},{R_{y} = {\tan^{- 1}\frac{- c_{1}}{\sqrt{a_{1}^{2} + b_{1}^{2}}}}},{R_{z} = {\tan^{- 1}\frac{c_{2}}{{a_{1}b_{2}} - {a_{2}b_{1}}}}},$wherein a₁, b₁, c₁, a₂, b₂, c₂ are obtained when solving the unit vectorof the positive direction of the X-axis and the positive direction ofthe Y-axis in the second coordinate system 220, and substituting thevalue of a₁, b₁, c₁, a₂, b₂ and c₂ into the expression of the rotationoffset defined as get the result of the final rotation offset.

The method for measuring the pose of the robotic end tool provided bythe present application, the method establishes a first coordinatesystem 210 and a second coordinate system 220 at the center of theflange 21 and the center of the end tool 22 respectively, calculates apositional offset of the origin of the second coordinate system 220relative to the origin of the first coordinate system 210, andcalculates a rotational offset of the second coordinate system 220relative to the first coordinate system 210 by the posturetransformation matrix of the second coordinate system 220, thereforeobtains the pose of the end tool 22 relative to the flange 21, themethod for measuring the pose obtains the pose of the end tool 22 bycalculating the relative position and relative posture of the end tool22 and the flange 21, and the precision and stability of the posemeasurement method are high.

It's obvious that the aforementioned embodiments are only preferredembodiments of the present application, and are not intended to limitthe present application. Any modification, equivalent replacement,improvement, and so on, which are made within the spirit and theprinciple of the present application, should be comprised in the scopeof the present application.

What is claimed is:
 1. A method for measuring a pose of a robotic endtool, comprising: obtaining a three-dimensional feature of a flange forclamping the end tool and a three-dimensional feature of the end tool;determining a center of the flange according to the three-dimensionalfeature of the flange, determining a center of the end tool according tothe three-dimensional feature of the end tool; establishing a firstcoordinate system and a second coordinate system based on the center ofthe flange and the center of the end tool acting as the origin of firstcoordinate system and the origin of the second coordinate systemrespectively; calculating a positional offset of the origin of thesecond coordinate system relative to the origin of the first coordinatesystem; in the first coordinate system, calculating a unit vector in apositive direction of the X-axis, a unit vector in a positive directionof the Y-axis, and a unit vector in a positive direction of the Z-axisof the second coordinate system; and collectively forming a posturetransformation matrix of the second coordinate system by the unit vectorof the positive direction of the X-axis, the unit vector of the positivedirection of the Y-axis, and the unit vector of the positive directionof the Z-axis of the second coordinate system, and calculating arotation offset of the second coordinate system relative to the firstcoordinate system by the posture transformation matrix.
 2. The method ofclaim 1, wherein the step of calculating the positional offset of theorigin of the second coordinate system relative to the origin of thefirst coordinate system particularly comprising: defining the origin ofthe first coordinate system as 0₁, defining the origin of the secondcoordinate system as 0₂, and defining a coordinate value of 0₁ in thefirst coordinate system as (0, 0, 0), and defining a coordinate value of0₂ in the first coordinate system as (x₀, y₀, z₀); and calculating thepositional offset as Δx=x₀, Δy=y₀, Δz=z₀, wherein the Δx is thepositional offset of the second coordinate system relative to the firstcoordinate system in the X direction, the Δy is the positional offset ofthe second coordinate system relative to the first coordinate system inthe Y direction, and the Δz is the positional offset of the secondcoordinate system relative to the first coordinate system in the Zdirection.
 3. The method of claim 2, wherein the step that in the firstcoordinate system, calculating a unit vector in a positive direction ofthe X-axis of the second coordinate system, a unit vector of in positivedirection of the Y-axis, and a unit vector of in positive direction ofthe Z-axis specifically comprising: taking points P₁ and P₂ on theX-axis and the Y-axis of the second coordinate system respectively, anddefining coordinate values of P₁ and P₂ in the first coordinate systemas (x₁, y₁, z₁) and (x₂, y₂, z₂) respectively; calculating the vector{right arrow over (O₂P₁)}=(x₁−x₀, y₁−y₀, z₁−z₀), and calculating thevector {right arrow over (O₂P₂)}=(x₂−x₀, y₂−y₀, z₂−z₀); calculating aunit vector {right arrow over (X)} of the {right arrow over (O₂P₁)} as$\left( {\frac{x_{1} - x_{0}}{\sqrt{\left( {x_{1} - x_{0}} \right)^{2} + \left( {y_{1} - y_{0}} \right)^{2} + \left( {z_{1} - z_{0}} \right)^{2}}},\frac{y_{1} - y_{0}}{\sqrt{\left( {x_{1} - x_{0}} \right)^{2} + \left( {y_{1} - y_{0}} \right)^{2} + \left( {z_{1} - z_{0}} \right)^{2}}},\frac{z_{1} - z_{0}}{\sqrt{\left( {x_{1} - x_{0}} \right)^{2} + \left( {y_{1} - y_{0}} \right)^{2} + \left( {z_{1} - z_{0}} \right)^{2}}}} \right)$wherein the {right arrow over (X)} is a unit vector of the secondcoordinate system in the positive direction of the X-axis; calculating aunit vector {right arrow over (Y)} of the {right arrow over (O₂P₂)} as$\left( {\frac{x_{2} - x_{0}}{\sqrt{\left( {x_{2} - x_{0}} \right)^{2} + \left( {y_{2} - y_{0}} \right)^{2} + \left( {z_{2} - z_{0}} \right)^{2}}},\frac{y_{2} - y_{0}}{\sqrt{\left( {x_{2} - x_{0}} \right)^{2} + \left( {y_{2} - y_{0}} \right)^{2} + \left( {z_{1} - z_{0}} \right)^{2}}},\frac{z_{2} - z_{0}}{\sqrt{\left( {x_{1} - x_{0}} \right)^{2} + \left( {y_{1} - y_{0}} \right)^{2} + \left( {z_{2} - z_{0}} \right)^{2}}}} \right)$wherein the {right arrow over (Y)} is a unit vector of the secondcoordinate system in the positive direction of the Y-axis; andcalculating a unit vector {right arrow over (Z)} of the secondcoordinate system in the positive direction of the Z-axis as {rightarrow over (X)}×{right arrow over (Y)}.
 4. The method of claim 1,wherein the unit vector in the positive direction of the X-axis of thesecond coordinate system is defined as (a₁, b₁, c₁), and the unit vectorin the positive direction of the Y-axis of the second coordinate systemis defined as (a₂, b₂, c₂), the unit vector in the positive direction ofthe Z-axis of the second coordinate system is defined as (a₃, b₃, c₃),and the posture transformation matrix is calculated to be$\begin{bmatrix}a_{1} & a_{2} & a_{3} \\b_{1} & b_{2} & b_{3} \\c_{1} & c_{2} & c_{3}\end{bmatrix}.$
 5. The method of claim 4, wherein the rotation offsetsare${R_{x} = {\tan^{- 1}\frac{b_{1}}{a_{1}}}},{R_{y} = {\tan^{- 1}\frac{- c_{1}}{\sqrt{a_{1}^{2} + b_{1}^{2}}}}},{R_{z} = {\tan^{- 1}\frac{c_{2}}{c_{3}}}},$wherein the R_(x) is a rotational offset of the second coordinate systemrelative to the first coordinate system on the X-axis, and the R_(y) isa rotational offset of the second coordinate system relative to thefirst coordinate system on the Y-axis, the R_(z) is a rotational offsetof the second coordinate system relative to the first coordinate systemon the Z-axis.
 6. The method of claim 1, wherein the three-dimensionalfeatures of the flange and the end tool are obtained by a binocularthree-dimensional scanner.